Note: This site is not up to date right now! The site needs an update to handle the different forms of Pokémon. But unfortunately I have currently no time for that. Until then, please use our spreadsheet which I have already updated: Pogomoves Google Spreadsheet
What are IVs?

Each distinct species has three different base values: Attack, Defense and Stamina. These basic stats are the same for each distinct species. You can find them on the Base Stats Ranking. But there are individual values (IVs) for those three stats, too. These range from 0-15, are distributed randomly and hidden in the game. But you can calculate them with CP, HP and Stardust for PowerUp. If youre Pokemon got 15 on each stat, it is 100% perfect and will have the max CP on max level.

How important are IVs?

IVs are important if you want to powerup your Pokémon. Because a Pokémon with higher IVs will have a higher CP value at max level. If you dont want to powerup your Pokémon you should prefer the CP value. Because a 2000 CP Vaporeon with 10% IVs wins against a 1000 CP Vaporeon with 100% IVs. But if you powerup the 1000 CP Vaporeon it will be higher than the 2000 CP Vaporeon at the end.

* Each Pokémon has a secret level which can be approximately determined by stardust for powerup. If you powerup the Pokémon it comes a half level higher. That's why Pokémon also can have half levels. But when you catch a Pokémon, it will never be a half-level. This helps to narrow down the stats because we mustnt consider the half-levels.